Boston’s building boom is bringing more affordable housing to some of its most affluent neighborhoods.

A city program requiring developers to include low-cost apartments in or near their buildings has created more than 400 units of affordable housing in the Seaport and in South Boston since 2000, according to new figures released by the city this week. Nearly 430 more have come in the South End and several neighborhoods in downtown Boston.

That’s according to a report the city issued Monday on Boston’s Inclusionary Development Policy, which Mayor Martin J. Walsh’s administration is touting as a key tool in its bid to share the wealth of the city’s surging development. It found that, since 2000, private developers have built 1,737 apartments and condos citywide that were set at affordable prices.

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It’s a relatively small slice of the roughly 27,000 housing units Boston added between 2000 and 2015. The Menino Administration came under fire at various times for failing to hold developers to the program’s requirements, or to distribute money it collected.

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Its use has accelerated under Walsh, amid a surge in construction and changes to the program in 2015 that pushed many developers to pay more into city housing funds, if they choose not to include affordable units in their own buildings.

Of the 1,737 units created since 2000, 226 were finished last year; nearly 750 more are now under construction.

“We’ve made some significant inroads when it comes to affordable housing,” Walsh said.

Because the program is tied to private development, it tends to create the most affordable housing in parts of town that are seeing the most market-rate construction.

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In recent years, that has meant South Boston and the Seaport, the South End — especially along Harrison Avenue — and a cluster of downtown neighborhoods that have seen a flurry of high-rise apartments built. Together, those three areas have had 841 affordable units created under the program — nearly half the citywide total. By contrast, Roxbury, Roslindale, and Mattapan, which have seen far less market-rate construction, combine for 36 IDP units.

City officials said they were glad to see the addition of low-cost units in more expensive neighborhoods because they otherwise have few sites available to build more traditional affordable housing. They’ve also raised $97 million — $23.7 million of it last year after changes to the program — from developers who pay into a city housing fund instead of putting the affordable units in their own building. That money has helped finance another 1,070 units across the city, many built by affordable-housing developers in less-expensive neighborhoods such as Roxbury and Dorchester.

For residents, the affordable apartments cost the same no matter what neighborhood they’re in. For a typical one-bedroom apartment in the program, a couple earning $58,000 a year would pay $1,267 a month in rent.

Boston expects more new affordable units to come online in outlying neighborhoods, too, as more housing developers push to farther corners of the city in search of lower-cost land. The point, said Brian Golden, director of the Boston Planning & Development Agency, is to help encourage economic diversity across the city and make sure all of Boston feels the benefits from new development.

“We have helped thousands of residents and families find housing,” Golden said. “It’s critical that this building boom reaches every one of our residents.”